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Ho:p=0.67 H1: p does not equal 0.67 n=598 with 419 successes what is test stat for...

Ho:p=0.67

H1: p does not equal 0.67

n=598 with 419 successes

what is test stat for this sample?

what is thep-value?

with significant level of 0.01

Solutions

Expert Solution

We have to test the hypothesis that

Ho : P = 0.67 against H₁: P # 0.67 ( two-tailed test)

Given : n = 598

X: Observed number of successes = 419

p : sample proportion = 419/ 598 = 0.7126

Sampling distribution of proportion normal

p ~ N ( P, P(1-P) /n)

E(p) = P = 0.67 and SD(P) = sqrt( P * (1-P) /n) = sqrt ( 0.67 *0.33 /598) = 0.0192

The value of test statistic is

z = (p- E(p)) / SD(p) ~ N(0,1)

z = ( 0.7126 - 0.67 ) / 0.0192

z = 2.2187

Value of test statistic z = 2.2187

Since the test is two tailed and value of test statistic is 2.2187, p-value is obtained by

p-value = 2* P ( Z >2.2187)

from normal probability table

P ( Z > 2.2187) = 0.0133

p-value = 0.0266

Alpha: level of significance = 0.01

Decision: since p-value is greater than level of significance alpha, we failed to reject Ho.

Conclusion : There is not sufficient evidence support to claim the population proportion differs from 0.67.

milcah answered 2 hours ago

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